发帖
雷达卡
英文标题：
《An analytic recursive method for optimal multiple stopping: Canadization
and phase-type fitting》
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作者：
Tim Leung and Kazutoshi Yamazaki and Hongzhong Zhang
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最新提交年份：
2015
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英文摘要：
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence the solutions in general cannot be attained analytically. Motivated by the maturity randomization (Canadization) technique by Carr (1998), we approximate the refraction times by independent, identically distributed Erlang random variables. In addition, fitting random jumps to phase-type distributions, our method involves repeated integrations with respect to the resolvent measure written in terms of the scale function of the underlying Levy process. We derive a recursive algorithm to compute the value function in closed form, and sequentially determine the optimal exercise thresholds. A series of numerical examples are provided to compare our analytic formula to results from Monte Carlo simulation.
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中文摘要：
研究了由谱负Levy过程驱动的呼叫类型支付的最优多重停止问题。停止时间由恒定折射时间分隔，贴现率可以为正或负。计算涉及列维过程在恒定视界上的分布，因此通常无法通过解析方法获得解。受Carr（1998）提出的成熟度随机化（Canadization）技术的启发，我们使用独立、同分布的Erlang随机变量来近似折射时间。此外，为了将随机跳跃拟合到相位型分布，我们的方法涉及对根据潜在Levy过程的标度函数编写的预解测度的重复积分。我们推导了一个递归算法来计算封闭形式的值函数，并依次确定最佳运动阈值。通过一系列数值算例，将我们的解析公式与蒙特卡罗模拟结果进行了比较。
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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